Pre-Calculus 12 Notes

By: Gen L.

In partnership with Hyperion University, 2024

Lesson 1: Plotting Trigonometric Functions

The Unit Circle

On the unit circle:

Plotting Points

Using the points on the unit circle, plot these graphs:

Sine Graphs

Characteristics:

  • -int: 0
  • Period: , QP:
  • Amplitude: 1
  • Extrema:
  • Pattern: 0, 1, 0, -1
  • Note:

Cosine Graphs

Characteristics:

  • -int: 0
  • Period: , QP:
  • Amplitude: 1
  • Extrema:
  • Pattern: 1, 0, -1, 0
  • Note:

Transformations

Transforming a trig graph is similar to transforming a polynomial.

  • : Amplitude (Vertical Stretch)
  • : Period Factor (Horizontal Stretch)
  • : Phase Shift (Horizontal Translation)
  • : Central Axis Displacement (Vertical Translation)

Determining Transformations

Determine the Following:
2 3 - -
1 - 1
-3 1 -
2 3 1
-3 - -2

The Period

When I was explaining , I called it the period factor.

The Period is actually or .

Next Lesson